CBSE Board exams are starting in February, so guys, we have bought some of the CBSE Board Class 10 Math Important Question 2024. Solve these questions; it will help you guys revise the syllabus quickly and help you get good grades in your examination.
You can also check the other important subjects, such as English, Science, and all other subjects.
CBSE Board Class 10 Math Important Question 2024: Objective
1. If two positive integers p and q can be expressed as p = ab and q = ab; a, b being prime numbers, then LCM (p, q) is.
(a) ab
(b) a²b2
(c) a³b2
(d) a³b³
2. What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact number of hours?
(a) 17 km/hours
(c) 13 km/hours
(b) 7 km/hours
(d) 26 km/hours
3. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?
(a) 144
(b) 128
(c) 288
(d) 272
4. If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is.
(a) 2
(b) 4
(c) 6
(d) 8
5. 36 can be expressed as a product of its primes as.
(a) 22 x 32
(b) 21 x 33
(c) 2 x 3
(d) 2° x 3″
6. 7× 11 × 13 × 15+15 is a.
(a) Prime number
(b) Composite number
(c) Neither prime nor composite.
(d) None of the above
7. If p and q are positive integers such that p = ab and q= a²b, where a, b are prime numbers, then the LCM (p, q) is.
(a) ab
(b) a²b²
(c) ab
(d) a³b³
8. In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are.
(a) 14
(b) 12
(c) 16
(d) 18
9. What is the minimum number of rooms required during the event?
(a) 11
(b) 31
(c) 41
(d) 21
10. The LCM of 60, 84 and 108 is.
(a) 3780
(b) 3680
(c) 4780
(d) 4680
11. The product of HCF and LCM of 60,84 and 108 is
(a) 55360
(b) 35360
(c) 45500
(d) 45360
12. 108 can be expressed as a product of its primes as.
(a) 23 x 32
(b) 2 x 3
(c) 22 x 32
(d) 22 x 33
13. The two zeroes in the above shown graph are.
(a) 2, 4
(b) -2, 4
(c) 8, 4
(d) 2,-8
14. If the fixed charges of auto rickshaw be Rs x and the running charges be Rs y km/hr, the pair of linear equations representing the situation is.
(a) x+10y=110, x + 15y = 75
(b) x+10y=75, x+15y110
(c) 10x+y=110, 15x+y=75
(d) 10x+y=75, 15 x + y =110
15. A person travels a distance of 50km. The amount he has to pay is.
(a) Rs.155
(b) Rs.255
(c) Rs.355
(d) Rs.455
CBSE Board Class 10 Math Important Question 2024: Subjective
1. In an AP, if a = 50, d-4 and S₁ = 0, then find the value of n.
2. Find the sum of the first twelve 2-digit multiples of 7, using an AP.
3. A solid metallic sphere of radius 3 cm is melted and recast into the shape of a solid cylinder of radius 2 cm. Find the height of the cylinder.
4. Find the nature of the roots of the quadratic equation x²-5x+9=0.
5. Write a quadratic equation with roots-3 and 5.
6. Solve the quadratic equation 2x²-5x-1=0 for x.
7. In Figure 1, if tangents PA and PB drawn from a point P to a circle with centre O, are inclined to each other at an angle of 70°, then find the measure of POA.
8. A spherical glass vessel has a cylindrical neck 8 cm long and 1 cm in radius. The radius of the spherical part is 9 cm. Find the amount of water (in litres) it can hold, when filled completely.
9. From a solid cylinder, whose height is 2-4 cm and diameter 1-4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.
10. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
11. How many terms are there in A.P. whose first and fifth term are -14 and 2, respectively and the last term is 62.
12. From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the centre of the circle bisects the angle between the two tangents.
13. Find the value of ‘p’ for which one root of the quadratic equation px-14x+80 is 6 times the other.
14. If one zero of the polynomial p(x)= 6x²+37x-(k-2) is reciprocal of the other, then find the value of k.
15. Two numbers are in the ratio 2:3 and their LCM is 180. What is the HCF of these numbers?
16. If a fair coin is tossed twice, find the probability of getting ‘atmost one head.
17. In Figure 2, the angles of elevation of the top of a tower AB of height ‘h’ m, from two points P and Q at a distance of x m and y m from the base of the tower respectively and in the same straight line with it, are 60° and 30°, respectively. Prove that h² = xy.
18. A straight highway leads to the foot of a tower. A man standing on the top of the 75 m high tower observes two cars at angles of depression of 30 and 60, which are approaching the foot of the tower. If one car is exactly behind the other on the same side of the tower, find the distance between the two cars. (use 3-1.73)
19. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30. Determine the height of the tower.
20. How many two digits numbers are divisible by 3?
21. Find the value of (sin² 33″ + sin² 57″)
22. Find the ratio in which the segment joining the points (1, 3) and (4, 5) is divided by x-axis? Also find the coordinates of this point on x-axis.
23. If S, the sum of first a terms of an AP is given by S,,=3n²-4n, find the ath term.
24. Show that every positive odd integer is of the form (4q+1) or (4q+3), where q is some integer.
25. Do you know old clothes which are thrown as waste not only fill the landfill site but also produce very harmful greenhouse gas. So, it is very important that we reuse old clothes in whatever way we can. The picture given below on the right, shows a footmat (rug) made out of old t-shirts yarn. Observing the picture, you will notice that a number of stitches in circular rows are making a pattern: 6, 12, 18, 24, .
Based on the above information, answer the following questions:
(a) Check whether the given pattern forms an AP. If yes, find the common difference and the next term of the AP.
(b) Write the nth term of the AP. Hence, find the number of stitches in the 10th circular row.
